The major purpose of this research is to formulate the best way that sequential designs can be implemented in clinical trials when the major endpoint of interest is length of survival. We propose to develop a computer algorithm which will find the sequential design which minimizes either total accrual or time to termination of a study, while still preserving the overall level of significance and power to detect a clinically significant difference. We also propose to develop methodology for deriving the exact sequential distribution of nonparametric test statistics, computed after groups of observations. This will be used for deriving exact group sequential tests with studies that have moderate sample size. Finally, we will investigate the bias of fixed sample inference following a group sequential test and indicate how to adjust the inference to minimize the bias.